English

Double-Layer Potentials for a Generalized Bi-Axially Symmetric Helmholtz Equation II

Analysis of PDEs 2018-07-11 v1

Abstract

The double-layer potential plays an important role in solving boundary value problems for elliptic equations. All the fundamental solutions of the generalized bi-axially symmetric Helmholtz equation were known, and only for the first one was constructed the theory of potential. Here, in this paper, we aim at constructing theory of double-layer potentials corresponding to the next fundamental solution. By using some properties of one of Appell's hypergeometric functions in two variables, we prove limiting theorems and derive integral equations concerning a denseness of double-layer potentials.

Keywords

Cite

@article{arxiv.1807.03639,
  title  = {Double-Layer Potentials for a Generalized Bi-Axially Symmetric Helmholtz Equation II},
  author = {Abdumauvlen Berdyshev and Anvar Hasanov and Tuhtasin Ergashev},
  journal= {arXiv preprint arXiv:1807.03639},
  year   = {2018}
}

Comments

10 pages. arXiv admin note: substantial text overlap with arXiv:0810.3979

R2 v1 2026-06-23T02:56:21.747Z